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Basic 11 High Knudsen Number Flows Prof. T. NiimiCOE for Education and Research of Micro-Nano Mechatronics, Nagoya University

Basic 11High Knudsen Number Flows

Prof. T. NiimiDept. of Micro/Nano Systems Engineering

Nagoya University


1. High Knudsen Number Flows2. Development of Optical Diagnostics Methods for High Knudsen Number Flows

Laser Induced Fluorescence (LIF) : Resonantly Enhanced Multi-Photon Ionization (REMPI)

Rotational Nonequilibrium in Low Density N2 Jets3. Application of Pressure Sensitive Paint (PSP)

to High Knudsen Number FlowsDevelopment of PSP for Low Density Gas Flows Development of PSMF for Micro- and Nano-Devices

(PSMF: Pressure Sensitive Molecular Film )LB Method for Fabrication of PSMF Application of PSMF to Micro-Flows

4. Applications of PSP in Atmospheric ConditionRotating DisksMixing Chamber

Contents


λ1

λ2 λ 3

Large λ

Ex. Low Density Gas Flows

LEx. Micro System

Small L

Knudsen numberKn=λ/L

λ：Mean Free PathL：Characteristic Dimension

Continuum approach invalidKn larger than ~0.1

→ “ High Kn Number Flow ”(Large λ or Small L )

Flow field is strongly influenced by interaction of molecules with a solid boundary rather than intermolecular collisions

High Knudsen Number Flows


Loschmit’s NumberThe molecular number density of an ideal gas at standardcondition [0oC，1 atm(=760 Torr =760 mmHg)] in 1 cm3

n=2.68699×1019 cm-3

nd 221π

λ =

Mean free path in atmospheric pressure conditionAir: single molecular gas, mean diameter of a molecule d=3.7×10-10 m

λ=6.1×10-8 m ( 61 nm )

From the equation of state p=nkT (p: pressure，T: Temp.，k:Boltzmann’s const.)

λ is inversely proportional to P and proportional to T

Mean Free PathAverage distance that a molecule travels between successive collisions

d : diameter of a moleculen : number density

pT∝λ

Mean Free Path


International Symposium on Rarefied Gas Dynamics (since 1958)Rarefied Gas Dynamics (RGD) has developed along with space technologies from 1950’s and expanded into analyses of low density gas flows in vacuumtechnologies (such as semiconductor film growth)

Rarefied Gas FlowAtomic/Molecular Gas Flow◆Continuum Approach invalid

Analyses by Boltzmann Eq.Direct Simulation Monte Carlo (DSMC)

◆Nonequilibrium Phenomena◆Strong Influence of Interface

Accommodation CoefficientAdsorption ProbabilityPhysical Models of Solid Surface

Traditional High Knudsen Number Flow Rarefied Gas Flow or Atomic/Molecular Gas Flow


In so-called nano-technologies, attention has been focused mainly on fabrication of devices, but not on gas-surface interaction which is important for the devices working in ambient gas.

“High Knudsen Number Flow”

Flows around the micro-devices are also in the category of “Rarefied gas flows”, but it is difficult to accept that because the devices work mainly in the atmospheric condition

From Rarefied Gas Flow to High Knudsen Number Flow


L

Small Number of Intermolecular CollisionsFlow field is strongly influenced by interaction of molecules with a solid boundary

Strongly Nonequilibrium Gas FlowsTechnologies related to

Ultra-High VacuumMean Free Path λ：large

Nano- and Micro-DevicesCharacteristic Dimension

L: small

High Kn Number Flows

Gas-Surface Interaction

Lack of Precise Experimental Data

Molecular Beam Flux of Scattered Molecules

High Knudsen Number Flows


Analyses of Flow Filed Structures and Nonequilibrium Phenomena of the Low Density Gas Flows

Developments of Measurement Techniques using interaction of Laser Beams with MoleculesMeasurement Techniques in Molecular Level:

LIF, CARS, DFWM, REMPI

Database Creation for Gas-Surface InteractionMomentum and Energy Accommodation Coefficients

Experiments using a Molecular Beam and Detection of Reflected Gas Molecules including Internal Energy by use of REMPI

Pressure Distribution on Solid Surfaces in High Knudsen Number FlowsWe can not Apply Pressure Taps to the Low Density Gas Flows and Micro- and Nano-Systems

Development of Measurement Techniques in Molecular Level: PSMF (Pressure Sensitive Molecular Film)

High Knudsen Number Flows Challenge of Our Group


LIFLaser Induced Fluorescence : I2, O2 and NO

Flow visualizationFujimotto, Niimi, Rarefied Gas Dynamics, AIAA(1988), 391-406Niimi; Protokoll des DLR-Kolloquiums LIF-8, (1996), 62-68Mori, Niimi, et al; AIAA paper 2005-1350, AIAA, 2005-01(USA, Reno)

Temperature measurement techniqueNiimi, et al; OPTICS LETTERS, 15-16(1990) , 918-920

Niimi, et al; Applied Optics, 34, 27(1995), 6275-6281 CARSCoherent Anti-Stokes Raman Scattering : N2 DFWMDegenerate Four Wave Mixing : I2 REMPIResonantly Enhanced Multi-Photon Ionization : N2

Mori, Niimi, et al; Physics of Fluids, 17, 117103(2005)

Development of Optical Diagnostic Methodsfor High Knudsen Number Flows


LIFLaser Induced Fluorescence of I2

Flow visualization of interacting supersonic free jetsRotational temperature measurement technique

REMPIResonantly Enhanced Multi-Photon Ionization : N2

Application of REMPI to highly rarefied gas flowsRotational nonequilibrium (non-Boltzmann distribution)

Development of Optical Diagnostic Methodsfor High Knudsen Number Flows


Absorption

Upper Energy Level

Fluorescence

Lower Energy Level

Principle of LIF A supersonic Ar-free jet visualized by I2-LIFNozzle Diameter: 0.5 mmPs/Pb= 150

Laser Induced Fluorescence


Nozzle

NozzleX

YZ

θ=45 deg

φ-shaped structure planar flow

Second cell

Flow field structure of two interacting supersonic free jets

Application of I2-LIF to Flow Visualization


θ=90 deg




θ=135 deg

stable unstable




θ=180 deg




Flow field structure of four interacting parallel

supersonic free jets

square arrangement of orifices intense expansion

orifice



Fluorescence intensity F (Two-Level Model)F= C[Aji/(Aji+Q)]BijIfNI2

Fluorescence intensity F1 when the I2 molecules in the rot. level J”1 are excitedF2 when the I2 molecules in the rot. level J”2 are excited

a ratio between these two fluorescence intensities F1/F2=[(Bij)1f1]/[(Bij)2f2],

C :a constant, Aji : spontaneous emission rate,Bij : stimulated-emission rate, Q : collision quenching rate, I : intensity of laser beam, NI2 : number density of I2, f : fraction of the ground-state population

If using common electronic and viblational state for F1 and F2,F1/F2=[S(J”1)fr(J”1,T)]/[ S(J”2)fr(J”2,T)]

S : Honl-London factor, fr : fraction of the rotational populationOnce two lines are selected, the ratio can be expressed as a function of temp.

..

Rotational Temperature Measurement using LIF


Temperature [K]

F 1/F

2 Wave Number Absorption Line

19432.0415 P(8)/R(10)28.0283 P(16)/R(18)26.6531 P(18)/R(20)19.6717 P(26)/R(28)14.0906 P(31)/R(33)

396.8701 P(43)/R(45)

Absorption lines of I2 moleculesin the transition of

Β 3Πou+ (v’=43) ← X 1Σg

+ ( v”=0 )

F1/F2 - Temperature


Ps=16 kPaPb=100 Pa

Fluorescence Intensity distribution depending on absorption lines

Supersonic free jets visualized by the use of irradiation of laser beams at wavelengths corresponding to the absorption lines


Distance [X/D]

Tem

pera

ture

[K]

Theory

Temp. overestimated : Thermal nonequilibrium

Rotational Temperature distribution along the centerline of a Supersonic Free Jet


Rotational Temperature Distribution of a Supersonic Free Jet

T. Niimi, et al, Optics Letters, 15-16(1990), 918-920 T. Niimi, et al, Applied Optics, 34, 27(1995), 6275-6281


Ground State

Resonance State

Ionization State

nR+m REMPI Process

n-photon

m-photon

Resonantly Enhanced Multi-Photon IonizationNon-intrusive Measurement Technique with High Sensitivity and Short Response，allowing measurement of non-equilibrium phenomena in the highly rarefied gas flows

Multi-Photon Ionization （MPI)Low Ionization Rate

(by 1 step)

REMPIHigh Ionization Rate

(by 2 steps)

・ Short Response・ High Sensitivity

for ２R＋２N2-REMPI109 molecules/cm3

REMPI


Objective of Our Study

Experimental detection of the non-Boltzmann distribution of the rotational levels (strongly nonequilibrium), applying the REMPI (Resonantly Enhanced Multi-PhotonIonization) method to the supersonic nitrogen free jets with P0D of 15 Torr-mm or lower.

P0D: Parameter depending inversely on nozzle Knudsen number P0 : stagnation pressureD : orifice diameter

Experimental Study of Rotational Nonequilibrium in Low Density N2 Jets using REMPI


Rotation（回転）

Vibration（振動）

Translation（並進）

Modes of Motion for Diatomic Molecule


Distributions for translational and rotational energies

Boltzmann distributions (thermodynamic equilibrium)

Rotational energyTranslational Velocity

Temperature is a determining factor of these distributions

Boltzmann Distributionof Translational Velocity(Nitrogen)

Boltzmann Distributionof Rotational Energy(Nitrogen)

[J ]Ttr: Translational temp. Trot: Rotational temp.

tr tr


2R+2 N2 REMPI Process

2-photon

2-photon

Ionization State

X1Σg+

a1Σg

Rotational Line Intensity

I J’,J’’=Cg(J’’)S(J’,J’’)exp(- Erot/kTrot)

C: constantg(J’’): nuclear spin degeneracyS(J’,J’’):2-photon

Honl-London factorErot : rotational energyk : Boltzmann’s constantTrot : rotational temperature

..

Resonantly Enhanced Multi-Photon IonizationNon-intrusive Measurement Technique with High Sensitivity and Short Response，allowing measurement of non-equilibrium phenomena in the highly rarefied gas flows

Photon energy is reduced to one-fourth of EBFThe ejected electrons by photons excite no other molecules or ions againNo consideration of the secondary electrons

2R+2 N2-REMPI


x

D=0.5mm

SonicNozzle

P0=30, 20, 10, 1 TorrPb=1.0x10-3-3.3x10-5 TorrT0=293 K

P0D=15, 10, 5, 0.5 Torr-mm

Ion detectionSecondary electron multiplier (P0=1 Torr)Tungsten Langmuir probe (P0≥10 Torr)

Experimental Apparatus


283 283.2 283.4 283.60

0.5

1

1.5R

EMPI

Sig

nal I

nten

sity

[a.u

.]

P0 · D = 15 Torr · mm x / D = 5.0 T0 = 293 K

O

Wavelength [nm]

25S

RQ

P

3 10

2 10

101

Step of wavelength: 0.001 nm

REMPI Spectrum


Rotational line intensity IJ’,J” in 2R+2 N2 -REMPI spectra

IJ’,J” = Ag(J”)S(J’,J”)N(J”)/(2J”+1)

N(J”) is proportional to (2J”+1)exp(–Erot/kTrot), provided that the rotational energy distribution follows the Boltzmann distribution.

IJ’,J” = Ag(J”)S(J’,J”)exp(–Erot/kTrot)Rotational temperature : slope of Boltzmann plot [ ln(IJ’,J”/gS)versus Erot/k], provided to be in equilibrium.Nonlinearity in the Boltzmann plot :

Rotational energy distribution deviates from the Boltzmann distribution(Non-Boltzmann distribution) Rotational temperature cannot be defined.

J : rotational quantum number (J’ : resonant state J” : ground state)

A : proportional constant independent of the rotational quantum N(J”): population number g(J”) : nuclear spin statistical weight (3 and 6 for odd and even J”)S(J’,J”) : two-photon Hönl-London factor

Boltzmann Plots


0 100 200 300 400 500 600-10

-8

-6

-4

-2

0

x/D 0.7 1.0 1.5 5.0 7.0 10.0 20.0

P0 · D = 15 Torr · mm T0 = 293 K

Erot /k [K]

J'' = 7

1112

131410

10

89

12

10

76

4 7

106

ln(I/

gS)

12

0 100 200 300 400

-8

-6

-4

-2

0

x/D 1.0 3.0 5.0 10.0 20.0

P0 · D = 10 Torr · mm T0 = 293 K

Erot /k [K]

ln(I/

gS)

10

J'' = 108

87

6

5

5

6

P0D=15 Torr-mm P0D=10 Torr-mm

Determination of the rotational temperature by using only the linear portion of the plots lying at smaller rotational quantum numbers

Boltzmann Plots


0 5 10 15 200

0.1

0.2

0.3 x/D

0.7 1.0 7.0 20.0

P0·D = 15 Torr · mm

Rotational quantum number J

Popu

latio

n ra

tio Trot =293 [K]

Temp. deduced by Boltzmann plot using only the data for smaller rot. Quantum number is usedfor Boltzmann distributions

Deviate from Boltzmann Distribution

distributions of x/D=7.0 and 20.0 for J”>7 shows the same tendencypartial freezing of the rot. population

Non-Boltzmann Distribution

Rotational Energy Distribution (P0·D = 15 Torr·mm)

H.Mori, T.Niimi et al.,Phys. Fluids 17, 117103 (2005)


Development of PSP for Low Density Gas


Model Surface

Excitation Light Luminescence

PSPLayer

Permeation

Diffusion

Oxygen Molecule

LuminophoreExcited

QuenchedLuminophore

Binder

Brighter region: Low pressure regionDarker region : High pressure region

Application of PSP in low-pressure regime is very few, because luminescence intensity does not change significantly in low- pressure range.

overcome the limitation of sensitivity!

Principle of PSP (Pressure Sensitive Paint)


• Sensitivity of PSP is restricted by gas permeability inside the binder layerPSPs have been regarded to be inappropriate for use in low pressure regime, because change of luminescence intensity is small.We have to overcome the limitation of sensitivity!

• 1st step: suitable binder?– Porous surface of anodized aluminum (AA):

luminescent molecules are bound directly on the surfaceexposed to the atmosphere : Bath‐Ru/AA

– poly(TMSP):glassy polymer with extremely high oxygen permeability :PtTFPP/poly(TMSP)

– (PtOEP/GP197: tested for comparison)

PSP in Low Pressure Regime


Xenon-Arc Lamp

Heat Absorbing Filter

Lens

Band-pass Filter

Optical Fiber

PSP Sample

Pure O2or

NO 1% + N2 99%

Turbo Molecular Pump

Scroll Pump

Personal Computer

Long-passFilter

(600nm)CCD-Camera &

Image Intensifier

Vacuum Chamber

Experimental Apparatus


0 50 100 1501

1.5

2In

vers

e In

tens

ity R

atio

I ref

/I

Pressure [Pa]

PtTFPP/poly(TMSP) Bath-Ru/AA PtOEP/GP197

Pref =1.0×10-2 Pa



• PtTFPP/poly(TMSP): high sensitivity high oxygen permeability of poly(TMSP)

• Bath‐Ru/AA: lower sensitivity than PtTFPP/poly(TMSP)time delay for abrupt pressure change

Adsorption and desorption of oxygen molecules inside pores

• PtOEP/GP197: no sensitivity



• 2nd step:Luminophore with high sensitivity to combine with the binder poly(TMSP)?

– PtTFPP (has been used)– PdOEP– PdTFPP

Oxygen Pressure Sensitivity of PSPs using poly(TMSP) as a Binder


(a) 1.0 × 10-2 – 1.3 × 102 [Pa] below 1 Torr (133.3 Pa)

(b) 1.3 × 102 – 1.3 × 104 [Pa]wide range of pressure

(1 – 100 Torr)

Luminophore:PdTFPP PdOEPPtTFPP

0 50 1000

5

10

15

Inve

rse

Inte

nsity

Rat

io I r

ef /I

Pressure [Pa]

Pref =1.0×10-2 Pa

0 5000 100000

5

10

15

Pressure [Pa]

Pref =1.3×102 PaInve

rse

Inte

nsity

Rat

io I r

ef /I



• PdOEP or PdTFPP / poly(TMSP)– very powerful measurement tool at low

pressure (< 1 Torr)– not suitable above 1 Torr (133Pa)

• PtTFPP / poly(TMSP)– useful at relatively wide pressure range

(up to 100 Torr)



(a) Ps =1.3 × 103 Pa (10 Torr)Pb =1.3 Pa (0.01 Torr)

2.7 × 101Pa

2.8 × 10-1Pa

1mm

PSP:PdOEP/poly(TMSP),test gas: oxygen

Ps: Source PressurePb: Background Pressure

Nozzle

(b) Ps =1.3 × 102 Pa (1Torr)Pb =7.7 × 10-2 Pa

2.5 × 100 Pa

1mm

1.4 × 10-2Pa

Nozzle

Pure O2 Jet

Solid Surface

PSP

φ0.53

60°

Pressure distribution below 1 Torr is detected !

Pressure Distribution on a Solid Surface interacting with Low Density Gas Flow


LB Method for Fabrication of PSMFApplication of PSMF to Micro-Flow

Development of PSMF for Micro- and Nano-Devices(PSMF: Pressure Sensitive Molecular Film )


μm50

Aggregation of luminescent molecules in the layer

For High Knudsen Number Flows:

PSMF（Pressure Sensitive Molecular Film）with nanometer order thickness and ordered molecular structure

Some problems forHigh Knudsen Number Flows

(the flow fields around micro-or nano-devices)

• Large thickness (>5µm)• Large surface roughness

(~µm)• Low spatial resolution

due to aggregation ofluminescent molecules

Conventional PSP


Compression

SubstrateConstant Pressure

Spread

1st layer2nd layer3rd layer4th layer

Amphiphilic molecule

Hydrophobic tail

Hydrophilic head

Random Ordered

Motion

Deposition

To fabricate the thin film with nanometer order

barrier

Piled layers (e.g. 4 layers)

Langmuir-Blodgett Method


•PdMP（Pd(II) Mesoporphyrin IX）-amphiphilic molecule-stable LB film can be obtained

PdOEP

PdMP

•PdOEP（Pd(II) Octaethylporphine）

prepare three types of samples2,6 and 20 layers of PSMF totest their pressure sensitivity

-conventional PSP composed of PdOEPhigh sensitivity in low pressure regime

-hydrophobic moleculedifficult to fabricate a stable LB film

Component of PSMF


1

1.1

1.2

1.3

1.4

0 30 60 90 120

Pressure [Pa]

Inve

rse

Inte

nsity

Rat

io I

ref /

I 2 Layers6 Layers20 Layers

1

1.1

1.2

1.3

1.4

0 30 60 90 120

Pressure [Pa]

Inve

rse

Inte

nsity

Pat

io I

ref /

I 2 Layers6 Layers20 Layers

PdOEP PdMP

Pref=1.0×10-2 [Pa] Pref=1.0×10-2 [Pa]

PSMF composed of PdMP has higher sensitivity than that of PdOEPThe sensitivity of 2-layer PSMF is higher than the others

PSMF has sufficient sensitivity in the low pressure regime with high Knudsen number

Pressure Sensitivity

Y. Matsuda et al., Experiments in Fluids Vol.42, No.4, pp.543-550 (2007)


Applicable Pressure Range<130Pa (pure O2)

Pd(II)Mesoporphyrin IX(PdMP)

NN

N N

Pd

O

OH

O

OH

MEMS Device used in Atmospheric Condition

Develop New PSMF with Higher Pressure Sensitivity

in Atmospheric Condition

Candidates of luminescent molecule for PSMFPtMP, PtMP-DME, PtPP, CuMP-DME

PSMF with Higher Pressure Sensitivity in Atmospheric Condition


NN

N NCu

O

O

O

O

NN

N N

Pt

O

OH

O

OH

Pt(II)Mesoporphyrin IX (PtMP)

NN

N NPt

O

OH

O

OH

Pt(II)Protoporphyrin IX (PtPP)

NN

N NPt

O

O

O

O

Pt(II)Mesoporphyrin IX-DME (PtMP-DME)

→ prepared 6-layers of PSMF for each luminescent molecule to test the pressure sensitivityin the range of pressure up to 21 kPa, partial pressure of oxygen in air

Cu(II)Mesoporphyrin IX-DME (CuMP-DME)

Luminescent Molecules


1

2

3

4

0 7 14 21Pressure [kPa]

I ref /

I

PtMPPtMP-DMEPtPPCuMP-DME

pref =1.0×10-2

PtMP has the highest pressure sensitivity below 21kPa

Stern-Volmer plot


24°

Micro-Conical Nozzle

to CCD Camera

Micro-Channel

137μm167μm

Xenon Lamp

Excitation Filter 400±20nm

Dichroic Mirror 500nm

Absorption Filter 600nm

Fluoresecnce microscope

Applications of PSMF to Micro-Scale Channel and Nozzle


Pressure distribution measured by PSMF

● PSMF • • • PSMF-PtMP 6-layer● Gas • • • O2 21.0%, N2 balance● Source pressure • • • 10.0kPa● Back pressure • • • 1.0kPa

Micro-Conical Nozzle

Y. Matsuda et al, Microfluidics and Nanofluidics,10, No.1, pp.165-171, 2011


Rotating DisksSurface Pressure Distribution

on Rotating Disks

Mixing ChamberDensity Fluctuation at Interface of Interacting Parallel Two Jets

Applications of PSP [PtTFPP/poly(TMSP)] in atmospheric condition


CMOScamera

Capacitancemanometer

Gas

Scroll pump

Revolutioncontroller

Revolutionsensor

Personalcomputer PC

LED excitationlight source

Vacuumchamber Model

atmospheric pressure

Three DisksPSP is painted on Top and Middle Disks

Experimental Setup

Top diskMiddle disk

Shroud

2.65mm5.00mm

95 mm95mm

0.30mm


Top Disk ⊿P=P2-P1=1.5kPa

Middle Disk ⊿P=3.0kPa

Disk Diameter : 95mmPSP: PtTFPP/poly(TMSP)，TiO2 2.0g/lCarrier Gas : N279%, O221%Rotating Speed (I) ：20000rpmRotating Speed of Reference Image (Iref) :300rpmIntegration Time:20msAmbient Pressure :100kPa

95

96

97

98

99

100

101

102

16 26 36 46Distance from rotating center[mm]

Pre

ssur

e[kP

a]

top disk 20000rpmmiddle disk 20000rpm

gas is pushed out of the central region due to the centrifugal force

Surface Pressure Distribution on Rotating Disks

Experimantal conditions

Top diskMiddle disk

Shroud

2.65mm5.00mm

95 mm95mm

0.30mm


Mixing ChamberDensity Fluctuation at Interface of Interacting Parallel Two Jets

Applications of PSP [PtTFPP/poly(TMSP)] in atmospheric condition


AirN2

Out

Base

Glass

Lid

0.3

R1/4

2

40

36

66

2022

22

22

18

4

34

36

20

66D=2

Mixing Chamber


CMOScamera

PC

LED excitationlight source

Flowchannel

Flow controller

AirN2 Flow controller

Digital Mass Flow CotrollerMQV0002(Yamatake Co. Ltd.)

Flow Rate：20ml/min~2000ml/minAccuracy：±10ml/min

(Q=20~1000ml/min)±20ml/min(Q=1000~2000ml/min)

Response Time：0.3s

PSPPtTFPP/poly(TMSP)・Relatively high sensitivity around

atmospheric pressure・High Oxygen Permeability, ・ Quick Time Response

Experimental Setup


Re=830(Q=1500ml/min)Re=550(Q=1000ml/min)Re=10(Q=20ml/min)

AirN2Flow Rate：Air:N2=1：1

Experimantal Results


1. High Knudsen Number Flows2. Development of Optical Diagnostics Methods for High Knudsen Number Flows

Laser Induced Fluorescence (LIF) : Resonantly Enhanced Multi-Photon Ionization (REMPI)

Rotational Nonequilibrium in Low Density N2 Jets3. Application of Pressure Sensitive Paint (PSP)

to High Knudsen Number FlowsApplications of PSP to Low Density Gas Flows, Development of PSMF for Micro- and Nano-Devices

(PSMF: Pressure Sensitive Molecular Film )LB Method for Fabrication of PSMF Application of PSMF to Micro-Flows

4. Applications of PSP in Atmospheric ConditionRotating DisksMixing Chamber

Summary

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